NumericalGradient.derivative

NumericalGradient.derivative(point)

Return the derivative in point.

The derivative of the gradient is often called the Hessian.

Parameters:

pointdomain element-like

The point that the derivative should be taken in.

Returns:

derivativeNumericalDerivative

Numerical estimate of the derivative. Uses the same method as this operator does, but with half the number of significant digits in the step size in order to preserve numerical stability.

Examples

Compute a numerical estimate of the derivative of the squared L2 norm:

>>> space = odl.rn(3)
>>> func = odl.solvers.L2NormSquared(space)
>>> grad = NumericalGradient(func)
>>> hess = grad.derivative([1, 1, 1])
>>> hess([1, 0, 0])
rn(3).element([ 2.,  0.,  0.])

Find the Hessian matrix:

>>> hess_matrix = odl.matrix_representation(hess)
>>> np.allclose(hess_matrix, 2 * np.eye(3))
True